Question: Simplify the following expression and state the condition under which the simplification is valid. $x = \dfrac{a^2 - 9}{a + 3}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = a$ $ b = \sqrt{9} = 3$ So we can rewrite the expression as: $x = \dfrac{({a} + {3})({a} {-3})} {a + 3} $ We can divide the numerator and denominator by $(a + 3)$ on condition that $a \neq -3$ Therefore $x = a - 3; a \neq -3$